4x(-3x+2)=7x-2

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Solution for 4x(-3x+2)=7x-2 equation:


Simplifying
4x(-3x + 2) = 7x + -2

Reorder the terms:
4x(2 + -3x) = 7x + -2
(2 * 4x + -3x * 4x) = 7x + -2
(8x + -12x2) = 7x + -2

Reorder the terms:
8x + -12x2 = -2 + 7x

Solving
8x + -12x2 = -2 + 7x

Solving for variable 'x'.

Reorder the terms:
2 + 8x + -7x + -12x2 = -2 + 7x + 2 + -7x

Combine like terms: 8x + -7x = 1x
2 + 1x + -12x2 = -2 + 7x + 2 + -7x

Reorder the terms:
2 + 1x + -12x2 = -2 + 2 + 7x + -7x

Combine like terms: -2 + 2 = 0
2 + 1x + -12x2 = 0 + 7x + -7x
2 + 1x + -12x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
2 + 1x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.1666666667 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.08333333333x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.08333333333x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.08333333333x + x2 = 0 + 0.1666666667
-0.08333333333x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-0.08333333333x + x2 = 0.1666666667

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 0.1666666667 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 0.1666666667 + 0.001736111111

Combine like terms: 0.1666666667 + 0.001736111111 = 0.168402777811
0.001736111111 + -0.08333333333x + x2 = 0.168402777811

Factor a perfect square on the left side:
(x + -0.04166666667)(x + -0.04166666667) = 0.168402777811

Calculate the square root of the right side: 0.410369075

Break this problem into two subproblems by setting 
(x + -0.04166666667) equal to 0.410369075 and -0.410369075.

Subproblem 1

x + -0.04166666667 = 0.410369075 Simplifying x + -0.04166666667 = 0.410369075 Reorder the terms: -0.04166666667 + x = 0.410369075 Solving -0.04166666667 + x = 0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = 0.410369075 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 0.410369075 + 0.04166666667 x = 0.410369075 + 0.04166666667 Combine like terms: 0.410369075 + 0.04166666667 = 0.45203574167 x = 0.45203574167 Simplifying x = 0.45203574167

Subproblem 2

x + -0.04166666667 = -0.410369075 Simplifying x + -0.04166666667 = -0.410369075 Reorder the terms: -0.04166666667 + x = -0.410369075 Solving -0.04166666667 + x = -0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = -0.410369075 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -0.410369075 + 0.04166666667 x = -0.410369075 + 0.04166666667 Combine like terms: -0.410369075 + 0.04166666667 = -0.36870240833 x = -0.36870240833 Simplifying x = -0.36870240833

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.45203574167, -0.36870240833}

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